DLMF:10.9.E2 (Q3067): Difference between revisions

From DRMF

Jump to navigation Jump to search

← Older edit

Revision as of 15:10, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 15:11, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint
(7 intermediate revisions by the same user not shown)
		Property / Symbols used
			Q10784
		Property / Symbols used: Q10784 / rank
			Normal rank
		Property / Symbols used: Q10784 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\in}}$ \in
		Property / Symbols used: Q10784 / qualifier
			xml-id: introduction.Sx4.p1.t1.r10.m2adec
		Property / Symbols used
			base of natural logarithm
		Property / Symbols used: base of natural logarithm / rank
			Normal rank
		Property / Symbols used: base of natural logarithm / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathrm{e}}}$ \expe
		Property / Symbols used: base of natural logarithm / qualifier
			xml-id: C4.S2.E11.m2adec
		Property / Symbols used
			imaginary unit
		Property / Symbols used: imaginary unit / rank
			Normal rank
		Property / Symbols used: imaginary unit / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathrm{i}}}$ \iunit
		Property / Symbols used: imaginary unit / qualifier
			xml-id: C1.S9.E1.m2adec
		Property / Symbols used
			Q10818
		Property / Symbols used: Q10818 / rank
			Normal rank
		Property / Symbols used: Q10818 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathbb{Z}}}$ \Integers
		Property / Symbols used: Q10818 / qualifier
			xml-id: introduction.Sx4.p2.t1.r20.m2adec
		Property / Symbols used
			Q10771
		Property / Symbols used: Q10771 / rank
			Normal rank
		Property / Symbols used: Q10771 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\int}}$ \int
		Property / Symbols used: Q10771 / qualifier
			xml-id: C1.S4.SS4.m3aadec
		Property / Symbols used
			sine function
		Property / Symbols used: sine function / rank
			Normal rank
		Property / Symbols used: sine function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\sin\NVar{z}}}$ \sin@@{\NVar{z}}
		Property / Symbols used: sine function / qualifier
			xml-id: C4.S14.E1.m2aadec
		Property / Symbols used
			Q11429
		Property / Symbols used: Q11429 / rank
			Normal rank
		Property / Symbols used: Q11429 / qualifier
			Defining formula: ${\displaystyle{\displaystyle n}}$ n
		Property / Symbols used: Q11429 / qualifier
			xml-id: C10.S1.XMD2.m1dec
		Property / Symbols used
			Q11426
		Property / Symbols used: Q11426 / rank
			Normal rank
		Property / Symbols used: Q11426 / qualifier
			Defining formula: ${\displaystyle{\displaystyle z}}$ z
		Property / Symbols used: Q11426 / qualifier
			xml-id: C10.S1.XMD6.m1adec

---

Latest revision as of 15:11, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:10.9.E2	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle J_{n}\left(z\right)=\frac{1}{\pi}\int_{0}^{\pi}\cos\left(z\sin\theta-n\theta\right)\mathrm{d}\theta=\frac{i^{-n}}{\pi}\int_{0}^{\pi}e^{iz\cos\theta}\cos\left(n\theta\right)\mathrm{d}\theta,}}$

0 references

DLMF id

DLMF:10.9.E2

0 references

constraint

${\displaystyle{\displaystyle n\in\mathbb{Z}}}$

0 references

Symbols used

Bessel function of the first kind

Defining formula

${\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}$

xml-id

C10.S2.E2.m2aadec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

${\displaystyle{\displaystyle\pi}}$

xml-id

C3.S12.E1.m2aadec

0 references

cosine function

Defining formula

${\displaystyle{\displaystyle\cos\NVar{z}}}$

xml-id

C4.S14.E2.m2aadec

0 references

Q10770

Defining formula

${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$

xml-id

C1.S4.SS4.m1aadec

0 references

Q10784

Defining formula

${\displaystyle{\displaystyle\in}}$

xml-id

introduction.Sx4.p1.t1.r10.m2adec

0 references

base of natural logarithm

Defining formula

${\displaystyle{\displaystyle\mathrm{e}}}$

xml-id

C4.S2.E11.m2adec

0 references

imaginary unit

Defining formula

${\displaystyle{\displaystyle\mathrm{i}}}$

xml-id

C1.S9.E1.m2adec

0 references

Q10818

Defining formula

${\displaystyle{\displaystyle\mathbb{Z}}}$

xml-id

introduction.Sx4.p2.t1.r20.m2adec

0 references

Q10771

Defining formula

${\displaystyle{\displaystyle\int}}$

xml-id

C1.S4.SS4.m3aadec

0 references

sine function

Defining formula

${\displaystyle{\displaystyle\sin\NVar{z}}}$

xml-id

C4.S14.E1.m2aadec

0 references

Q11429

Defining formula

${\displaystyle{\displaystyle n}}$

xml-id

C10.S1.XMD2.m1dec

0 references

Q11426

Defining formula

${\displaystyle{\displaystyle z}}$

xml-id

C10.S1.XMD6.m1adec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q3067&oldid=55149"